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Medical Imaging

Medical Imaging. Mohammad Dawood Department of Computer Science University of Münster Germany. Image Registration. Registration T : Transformation In this lecture Floating image : The image to be registered Target image : The stationary image. Registration Linear Transformations

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Medical Imaging

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  1. Medical Imaging Mohammad Dawood Department of Computer Science University of Münster Germany

  2. Image Registration

  3. Registration T : Transformation In this lecture Floating image : The image to be registered Target image : The stationary image

  4. Registration Linear Transformations - Translation - Rotation - Scaling - Affine

  5. Registration 3D Translation

  6. Registration 3D Rotation

  7. Registration 3D Scaling

  8. Registration Rigid registration Angles are preserved Parallel lines remain parallel

  9. Registration Affine registration

  10. Registration Feature Points

  11. Registration Feature Points 1. De-mean 2. Compute SVD 3. Calculate the transform

  12. Registration Feature Points Iterative Closest Points Algorithm (ICP) 1. Associate points by the nearest neighbor criteria. 2. Estimate transformation parameters using a mean square cost function. 3. Apply registration and update parameters.

  13. Registration Feature Points Random Sample Consensus Algorithm (RNSAC) 1. Transformation is calculated from hypothetical inliers 2. All other data are then tested against the fitted model and, if a point fits well to the model, also considered as a hypothetical inlier 3. The estimated model is reasonably good if sufficiently many points have been classified as hypothetical inliers. 4. The model is re-estimated from all assumed inliers 5. Finally, the model is evaluated by estimating the error of the inliers relative to the model

  14. Registration Phase Correlation

  15. Registration Distance Measures - Sum of Squared Differences (SSD) - Root Mean Square Difference (RMSD) - Normalized Cross Correlation (NXCorr) - Mutual Information (MI)

  16. Registration Sum of Squared Differences SSD(f,t) SSD(20f,t)

  17. Registration Root Mean Squared Differences RMS(f,t) RMS(20f,t)

  18. Registration Normalized Cross Correlation NXCorr(f,t) NXCorr(20f,t)

  19. Registration Mutual Information MI(f,t) MI(20f,t)

  20. Optical Flow

  21. Optical flow Brightness consistency constraint With Taylor expansion V : Flow (Motion)

  22. Optical flow Lucas Kanade Algorithm: Assume locally constant flow =>

  23. Optical flow Horn Schunck Algorithm: Assume globally smooth flow

  24. Optical flow Bruhn’s Non-linear Algorithm

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